Question

How do solve the following linear system?: `2x - 4y =3, 2x - 5y=3`?

Answer 1

`(1.5, 0)`

Explanation:

So first you can set up your linear system to the following:

`{(2x - 4y = 3), (2x - 5y = 3) :}`

Do this because it is visually easier to simplify the next couple steps.

For the simplification part, I will be using the elimination method on the `x` variables so that we can obtain a `y` variable answer.

Multiply the top equation in the linear system by `-1`

`-1(2x - 4y = 3)`
`2x - 5y = 3`

You should get the following when simplified:

`{(-2x + 4y = -3), (2x - 5y = 3) :}`

Next, add the equations together going vertically making sure to add only to the corresponding term.

The `x` values and the numerical values should be equal to `0` when this is done correctly and you should be left with the following:

`-y = 0`

Then simplify by dividing the `-1` coefficient from `y`:

`y = 0`

Then you plug the `y` value back into one of the original equations:

`2x - 4(0) = 3`

Then simplify:

`2x = 3`

Divide the `2` coefficient from the `x` and you should be just left with

`x = 3/2 = 1.5`

Finally, you plug them into a coordinate point that indicates when the two equations intersect:

`(1.5, 0)`